In the figure below, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of ∠POS and ∠SOQ, respectively. If ∠POS = x∘, find ∠ROT.
Ray OS stands on the line POQ, so that,
∠POS + ∠SOQ = 180∘
But, ∠POS = x∘
Hence, x∘+ ∠SOQ = 180∘
∠SOQ = 180∘ – x∘
Now, ray OR bisects POS.
Hence, ∠ROS = 12 × ∠POS = 12 × x∘ = x2∘
Similarly, ∠SOT =12 × ∠SOQ = 12 × ( 180∘ - x∘) = 90∘ – x2∘
∠ROT = ∠ROS + ∠SOT = x2∘ + 90∘ – x2∘ = 90∘